DLMF:18.12.E6 (Q5648)

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DLMF:18.12.E6
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    test
    Γ ⁡ ( λ + 1 2 ) ⁢ e z ⁢ cos ⁡ θ ⁢ ( 1 2 ⁢ z ⁢ sin ⁡ θ ) 1 2 - λ ⁢ J λ - 1 2 ⁡ ( z ⁢ sin ⁡ θ ) = ∑ n = 0 ∞ C n ( λ ) ⁡ ( cos ⁡ θ ) ( 2 ⁢ λ ) n ⁢ z n , Euler-Gamma 𝜆 1 2 superscript 𝑒 𝑧 𝜃 superscript 1 2 𝑧 𝜃 1 2 𝜆 Bessel-J 𝜆 1 2 𝑧 𝜃 superscript subscript 𝑛 0 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝜃 Pochhammer 2 𝜆 𝑛 superscript 𝑧 𝑛 {\displaystyle{\displaystyle\Gamma\left(\lambda+\tfrac{1}{2}\right)e^{z\cos% \theta}(\tfrac{1}{2}z\sin\theta)^{\frac{1}{2}-\lambda}J_{\lambda-\frac{1}{2}}% \left(z\sin\theta\right)=\sum_{n=0}^{\infty}\frac{C^{(\lambda)}_{n}\left(\cos% \theta\right)}{{\left(2\lambda\right)_{n}}}z^{n},}}
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    DLMF id
    DLMF:18.12.E6
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